Answer:
(f ∘ g)(-2) = 7
Step-by-step explanation:
Given:
[tex]f(x)=2x-3\\g(x)=-x+3[/tex]
The problem (49) is asking "What is f of g of x?" In simpler terms, we need to find [tex]g(-2)[/tex] and put that answer into [tex]f(x)[/tex]. Let's start by plugging in -2 to [tex]g(x)[/tex].
[tex]g(-2)=-(-2)+3\\g(-2)=2+3\\g(-2)=5[/tex]
We have now found out what [tex]g(-2)[/tex] is. We now have to input the answer we just got into [tex]f(x)[/tex] and solve for [tex]x[/tex].
[tex]f(5)=2(5)-3\\f(5)=10-3\\f(5)=7[/tex]
So our final answer would be:
(f ∘ g)(-2) = 7
